End mill having teeth and associated flutes with correlated physical parameters

ABSTRACT

An end mill includes a plurality of teeth and flutes. The teeth and their associated flutes include one or more correlated physical parameters. One such correlated parameter is that, at an axial location in a front half of an effective cutting length, at least one tooth of the plurality of teeth has a rake angle smaller than an average rake angle value of the plurality of teeth, and, at the same axial location, a flute preceding each such tooth has a helix angle larger than an average helix angle value of the plurality of flutes.

RELATED APPLICATIONS

This is a Continuation of U.S. patent application Ser. No. 14/880,440,filed Oct. 12, 2015, now U.S. Pat. No. 10,040,136. The contents of theabove-mentioned application are incorporated by reference, in theirentirety.

FIELD OF THE INVENTION

The subject matter of the present application relates to an end millconfigured for deep shouldering milling, and particularly a deepshouldering end mill capable of providing good quality surface finish onhigh hardness materials. The subject matter is particularly directed tosuch end mills having teeth and associated flutes with correlatedphysical parameters.

BACKGROUND OF THE INVENTION

End mills designed for shouldering applications, i.e. milling around anexternal periphery of a workpiece, typically have a maximum effectivecutting length of twice the diameter of the end mill (hereinafter “2D”;with similar length dimensions being represented similarly, e.g. two anda half times the diameter will be written as “2.5D” etc.). Unless statedto the contrary, references to end mill diameter in the specificationand claims refer to a diameter of the cutting portion at the cutting endface.

While in theory end mills can have any effective cutting length, inpractice it is exceedingly rare to find end mills that can milleffectively at a depth greater than 2D. This is because increasing depthexacerbates vibration of the end mill reducing both work piece surfacefinish and end mill tool life to standards lower than those accepted byindustry. To elaborate, end mills bend during shouldering, since the endmill is only held at one end thereof and the other end thereof is forcedagainst and impacts a rigidly held workpiece. Such impacts also cause arebound type effect, with this effect being comparatively greater withincreased end mill length.

Similarly this effect is also more severe when milling comparativelyharder workpiece materials since the milling forces exerted on the endmill are greater with each impact on the hard workpiece.

Another problem which is exacerbated with increased depth of milling ischip evacuation. To elaborate, large flute depth is most critical nearthe cutting end face since each chip is first contacted by the toothstarting near the cutting end face as it first enters the material. Thechip remains within the flute near the cutting end face forcomparatively more time than the remainder of the flute, since it onlyexits the flute when the end mill has rotated fully in the work pieceand the flute exits the workpiece allowing the chip to be ejected. Whilenot being bound by theory, if the flute is insufficiently sized tocontain the chip, abutment of the chip (which protrudes from theinsufficiently sized flute) against the end mill and workpiece canincrease vibration and even cause end mill breakage. It will beunderstood that with increased distance from the secured shank portionof the end mill this effect will be more significant.

Due to the high performance requirements in today's industry, what wasonce considered insignificant changes to end mill design are now able todefine whether an end mill is acceptable to industry standards ofsurface finish and chip removal or not. While any end mill cantheoretically machine any material, only by providing a competitive toollife for a given material removal rate and a desired level of surfacefinish can an end mill actually be considered relevant for a particularapplication.

SUMMARY OF THE INVENTION

In order to produce an end mill capable of deep shouldering milling(i.e. at a depth of at least 2.5D) while still providing good qualitysurface finish on high hardness materials, a number of vibrationreduction features have been incorporated into a single end mill. Eachinventive feature both alone and in combination is believed tosignificantly contribute to vibration reduction and consequentlyincrease tool life and surface finish achieved.

In accordance with a first aspect of the subject matter of the presentapplication, there is provided a finish end mill comprising a pluralityof teeth and flutes; wherein at an axial location in a front half of theeffective cutting length, at least one tooth of the plurality of teethhas a radial rake angle smaller than an average radial rake angle valueand a flute preceding each such tooth (i.e. each of said at least onetooth) has a helix angle larger than an average helix angle value of theplurality of flutes.

This geometry is believed to reduce vibration by providing teeth withdifferent radial rake angles while compensating at least one toothhaving a relatively smaller radial rake angle with a relatively largerhelix angle, the larger helix angle decreasing radial cutting forceneeded.

Stated differently, in accordance with a second aspect of the subjectmatter of the present application, there is provided a finish end millconfigured for rotating about a central rotation axis (A_(R)) definingopposite axially forward and rearward directions (D_(F), D_(R)), andopposite rotational preceding and succeeding directions (D_(P), D_(S)),the preceding direction (D_(P)) being the cutting direction, the endmill comprising: a shank portion; and a cutting portion extendingforward from the shank portion to a cutting end face; the cuttingportion comprising: an effective cutting length (L_(E)); a diameter(D_(E)); a plurality of integrally formed teeth; and a plurality offlutes alternating with the plurality of teeth, each flute having ahelix angle and a flute depth; each tooth comprising: a rake surface; arelief surface succeeding the rake surface and having a relief surfacewidth measurable in a plane perpendicular to the rotation axis (A_(R));a cutting edge formed at an intersection of the rake and reliefsurfaces; a relief edge spaced apart from the cutting edge and formed atan intersection of the relief surface and a flute surface of the flutesucceeding the tooth; and a tooth area defined between a first radialline extending from the cutting edge to the central rotation axis and asecond radial line extending from the central rotation axis to a nadirof the succeeding flute; wherein at an axial location in a front half ofthe effective cutting length: the flutes have an average helix anglevalue, with one or more flutes having a smallest helix angle value, andone or more flutes having a largest helix angle value; the teeth have anaverage radial rake angle value, with one or more teeth having asmallest radial rake angle value, and one or more teeth having a largestradial rake angle value; and, at least one tooth has a radial rake anglesmaller than the average radial rake angle value and the flute precedingeach such tooth has a helix angle larger than the average helix anglevalue.

In the first and second aspects, since the at least one tooth's radialrake angle is smaller than an average radial rake angle at the sameaxial location, and its associated flute's helix angle is larger than anaverage helix angle at the same axial location, the tooth's radial rakeangle can be considered to be negatively correlated with its associatedflute's helix angle.

In accordance with still another (third) aspect of the subject matter ofthe present application, there is provided a finish end mill comprisinga plurality of teeth and flutes: wherein at an axial location in a fronthalf of the effective cutting length, at least one tooth of theplurality of teeth has a tooth area greater than an average tooth areavalue of the plurality of teeth and a relief surface width smaller thanan average relief surface width value.

This geometry is believed to reduce vibration by providing differentgeometry teeth, while compensating structural weakness of a tooth with asmaller relief surface width by only reducing the width of teeth with acomparatively larger tooth area.

This geometry also allows an end mill to be provided with acomparatively larger flute, i.e. the flute preceding said tooth with acomparatively smaller relief surface, which is also believed to reducevibration by allowing more chip evacuation area as explained above.

Stated differently, in accordance with yet another (fourth) aspect ofthe subject matter of the present application, there is provided afinish end mill configured for rotating about a central rotation axis(A_(R)) defining opposite axially forward and rearward directions(D_(F), D_(R)), and opposite rotational preceding and succeedingdirections (D_(P), D_(S)), the preceding direction (D_(P)) being thecutting direction, the end mill comprising: a shank portion; and acutting portion extending forward from the shank portion to a cuttingend face; the cutting portion comprising: an effective cutting length(L_(E)); a diameter (D_(E)); a plurality of integrally formed teeth; anda plurality of flutes alternating with the plurality of teeth, eachflute having a helix angle and a flute depth; each tooth comprising: arake surface; a relief surface succeeding the rake surface and having arelief surface width measurable in a plane perpendicular to the rotationaxis (A_(R)); a cutting edge formed at an intersection of the rake andrelief surfaces; a relief edge spaced apart from the cutting edge andformed at an intersection of the relief surface and a flute surface ofthe flute succeeding the tooth; and a tooth area defined between a firstradial line extending from the cutting edge to the central rotation axisand a second radial line extending from the central rotation axis to anadir of the succeeding flute; wherein at an axial location in a fronthalf of the effective cutting length: the teeth have an average tootharea value, with one or more teeth having a smallest tooth area value,and one or more teeth having a largest tooth area value; the teeth havean average relief surface width value, with one or more teeth having asmallest relief surface width value, and one or more teeth having alargest relief surface width value; and, at least one tooth has a tootharea greater than the average tooth area value and a relief surfacewidth smaller than the average relief surface width value.

Notably, application of the inventive features of the aspects above arelocated at an axial location in a front half of the effective cuttinglength (i.e. a half of the effective cutting length which is distal froma shank of the endmill) since the problem of vibration is moresignificant with increased distance from a securely held shank of theend mill. It will be understood that their effectiveness is greater withincreasing distance from the shank (i.e. with increasing proximity tothe cutting end face). Nonetheless this is not to say that there wouldnot be any effect in a proximal half of the effective cutting length tothe shank.

In the third and fourth aspects, since the at least one tooth's tootharea has a larger than average tooth area value and its associatedrelief surface has a lower than average relief surface width value, thetooth's tooth area can be considered to be negatively correlated withits associated relief surface's relief surface width.

In accordance with still a further (fifth) aspect of the subject matterof the present application, there is provided a finish end millcomprising a shank and a cutting portion; the cutting portion having aneffective cutting length greater than 2.5D_(E) and comprising aplurality of teeth and flutes; the plurality of teeth comprising atleast two teeth having different radial rake angles, at least some ofthe different radial rake angle values being different from all othernon-identical values by 2° or more; and, each flute of the plurality offlutes have an increasing depth with increasing distance from the shank.

On the one hand this geometry provides an atypically long effectivecutting length while compensating for greater vibration associated withincreased cutting length by combining an enlarged flute depth distantfrom the shank with significantly different rake angles to reducevibration during milling.

In comparatively shorter end mills on the market, different rake anglesare often not cost effective due to their relatively small contributionin reducing vibration, at least in comparison to other vibrationreduction design options. However with longer end mills, and even moreso longer end mills with a large number of teeth (e.g. 5 or more teeth,and all the more so as the number of teeth increases), it has been foundthat providing different and particularly significantly varying theradial rake angles achieves a comparatively notable vibration reductioneffect, thereby justifying the added design complexity and expense ofproviding different radial rake angles.

Stated differently, in accordance with yet another (sixth) aspect of thesubject matter of the present application, there is provided a finishend mill configured for rotating about a central rotation axis (A_(R))defining opposite axially forward and rearward directions (D_(F),D_(R)), and opposite rotational preceding and succeeding directions(D_(P), D_(S)), the preceding direction (D_(P)) being the cuttingdirection, the end mill comprising: a shank portion; and a cuttingportion extending forward from the shank portion to a cutting end face;the cutting portion comprising: an effective cutting length (L_(E)); adiameter (D_(E)); a plurality of integrally formed teeth; and aplurality of flutes alternating with the plurality of teeth, each flutehaving a helix angle and a flute depth; each tooth comprising: a rakesurface; a relief surface succeeding the rake surface and having arelief surface width measurable in a plane perpendicular to the rotationaxis (A_(R)); a cutting edge formed at an intersection of the rake andrelief surfaces; a relief edge spaced apart from the cutting edge andformed at an intersection of the relief surface and a flute surface ofthe flute succeeding the tooth; and a tooth area defined between a firstradial line extending from the cutting edge to the central rotation axisand a second radial line extending from the central rotation axis to anadir of the succeeding flute; wherein at an axial location in a fronthalf of the effective cutting length: the teeth have an average radialrake angle value, with one or more teeth having a smallest radial rakeangle value, and one or more teeth having a largest radial rake anglevalue; wherein: the cutting portion has an effective cutting lengthgreater than 2.5D; at least some of the teeth with different radial rakeangle values have values different from all other non-identical valuesby 2° or more; and each flute of the plurality of flutes has anincreasing depth with increasing distance from the shank.

In the fifth and sixth aspects, a relatively large effective cuttinglength and relatively large difference between the radial rake anglevalues can be considered to be a positive correlation.

In accordance with a further (seventh) aspect of the subject matter ofthe present application, there is provided a finish end mill comprisinga shank and a cutting portion; the cutting portion comprising aplurality of teeth and flutes; the plurality of teeth comprising atleast three teeth having different radial rake angles, at least some ofthe different radial rake angle values being different from all othernon-identical values by 2° or more; and the plurality of flutes having ahelix variance of 6° or less.

On the one hand this geometry provides significantly different radialrake angles to reduce vibration during milling, compensating for thevery moderate helix angle variance (e.g. a helix angle variance of 6° orless). A large helix angle variance is believed to be a more effectivedesign option than varying rake angles, for vibration reduction. Someapplications where the disadvantage of moderate helix angle variationmay be beneficial are for particularly for comparatively long end mills(e.g. having an effective cutting length of at least 2.5D) and/or endmills with a comparatively large number of teeth (e.g. 5 or more teeth).

Stated differently, in accordance with yet another (eighth) aspect ofthe subject matter of the present application, there is provided afinish end mill configured for rotating about a central rotation axis(A_(R)) defining opposite axially forward and rearward directions(D_(F), D_(R)), and opposite rotational preceding and succeedingdirections (D_(P), D_(S)), the preceding direction (D_(P)) being thecutting direction, the end mill comprising: a shank portion; and acutting portion extending forward from the shank portion to a cuttingend face; the cutting portion comprising: an effective cutting length(L_(E)); a diameter (D_(E)); a plurality of integrally formed teeth; anda plurality of flutes alternating with the plurality of teeth, eachflute having a helix angle and a flute depth; each tooth comprising: arake surface; a relief surface succeeding the rake surface and having arelief surface width measurable in a plane perpendicular to the rotationaxis (A_(R)); a cutting edge formed at an intersection of the rake andrelief surfaces; a relief edge spaced apart from the cutting edge andformed at an intersection of the relief surface and a flute surface ofthe flute succeeding the tooth; and a tooth area defined between a firstradial line extending from the cutting edge to the central rotation axisand a second radial line extending from the central rotation axis to anadir of the succeeding flute; wherein at an axial location in a fronthalf of the effective cutting length: the flutes have an average helixangle value, with one or more flutes having a smallest helix anglevalue, and one or more flutes having a largest helix angle value; theteeth have an average radial rake angle value, with one or more teethhaving a smallest radial rake angle value, and one or more teeth havinga largest radial rake angle value; wherein, at an axial location in afront half of the effective cutting length: at least three teeth havingdifferent radial rake angles, at least some of the different radial rakeangle values being different from all other non-identical values by 2°or more, and the flutes having a helix variance of 6° or less.

In the seventh and eighth aspects, since relatively large differencebetween the radial rake angle values and a relatively small variance ofthe helix angles can be considered to be a negative correlation.

It should be understood that the term “negative correlation” in thespecification and claims should not be interpreted with a strictmathematical definition that as one variable increases the othercorrespondingly decreases, but rather should be understood in view ofthe disclosure and claims of the application, which generally describethis concept in connection with a physical object, specifically an endmill. A corresponding understanding should be similarly applied to any“positive correlation” in the specification and claims.

It will further be understood that the aspects, except where statedexplicitly, may also be beneficial for end mills of effective cuttinglength smaller than 2.5D.

Similarly, while the end mill according to the invention has beendesigned for finish applications, and primarily tested on high hardnessmaterials, it should be understood that it is believed that such endmill features, according to any of the aspects, may also be found to behighly effective for applications other than finish and even formachining less hard workpiece materials.

According to yet another (ninth) aspect, there is provided a finish endmill for configured for rotating about a central rotation axis (A_(R))defining opposite axially forward and rearward directions (D_(F),D_(R)), and opposite rotational preceding and succeeding directions(D_(P), D_(S)), the preceding direction (D_(P)) being the cuttingdirection, the end mill can comprise: a shank portion; and a cuttingportion extending forward from the shank portion to a cutting end face;the cutting portion comprising: an effective cutting length (L_(E)); adiameter (D_(E)); a plurality of integrally formed teeth; and aplurality of flutes alternating with the plurality of teeth, each flutehaving a helix angle and a flute depth; each tooth comprising: a rakesurface; a relief surface succeeding the rake surface and having arelief surface width measurable in a plane perpendicular to the rotationaxis (A_(R)); a cutting edge formed at an intersection of the rake andrelief surfaces; a relief edge spaced apart from the cutting edge andformed at an intersection of the relief surface and a flute surface ofthe flute succeeding the tooth; and a tooth area defined between a firstradial line extending from the cutting edge to the central rotation axisand a second radial line extending from the central rotation axis to anadir of the succeeding flute; wherein at an axial location in a fronthalf of the effective cutting length: the flutes have an average helixangle value, with one or more flutes having a smallest helix anglevalue, and one or more flutes having a largest helix angle value; theteeth have an average radial rake angle value, with one or more teethhaving a smallest radial rake angle value, and one or more teeth havinga largest radial rake angle value; the teeth have an average tooth areavalue, with one or more teeth having a smallest tooth area value, andone or more teeth having a largest tooth area value; and the teeth havean average relief surface width value, with one or more teeth having asmallest relief surface width value, and one or more teeth having alargest relief surface width value.

It will also be understood that the above-said is a summary, and thatany of the aspects above may further comprise any of the featuresdescribed hereinbelow. Specifically, the following features, eitheralone or in combination, may be applicable to any of the above aspects:

-   A. At an axial position in at least in the front half of the    effective cutting length, the flutes can have an average helix angle    value, with one or more flutes having a smallest helix angle value,    and one or more flutes having a largest helix angle value.-   B. At an axial position in at least in the front half of the    effective cutting length, the teeth can have an average radial rake    angle value, with one or more teeth having a smallest radial rake    angle value, and one or more teeth having a largest radial rake    angle value.-   C. At an axial position in at least in the front half of the    effective cutting length, the teeth can have an average tooth area    value, with one or more teeth having a smallest tooth area value,    and one or more teeth having a largest tooth area value.-   D. At an axial position in at least in the front half of the    effective cutting length, the teeth can have an average relief    surface width value, with one or more teeth having a smallest relief    surface width value, and one or more teeth having a largest relief    surface width value.-   E. An end mill can be configured for milling high hardness materials    (e.g. materials with a hardness of 38-65 HRc). For example, some    notable materials of this type can be those known as D2, H13 and    P20.-   F. An end mill can be configured for rotating about a central    rotation axis (A_(R)).-   G. A central rotation axis (A_(R)) can define opposite axially    forward and rearward directions (D_(F), D_(R)), and opposite    rotational preceding and succeeding directions (D_(P), D_(S)), the    preceding direction (D_(P)) being the cutting direction. It will be    understood that a “front half” of an effective cutting length is one    which is further in the forward direction than the remaining half.    Stated differently, the “front half” is a half distal from a shank.-   H. An end mill can comprise a shank portion and a cutting portion    extending forward from the shank portion to a cutting end face.-   I. An end mill, or more precisely a cutting portion of an end mill    can comprise an effective cutting length (L_(E)), a diameter    (D_(E)), a plurality of integrally formed teeth, and a plurality of    flutes alternating with the plurality of teeth, each of the flutes    having a helix angle and a flute depth. To clarify, the flutes may    have variable helix angles which change at different axial    locations, nonetheless at each axial location such as those shown in    FIGS. 3 to 6, there is a helix angle value. Additionally, the    diameter D_(E) may differ at different axial locations (denoted    herein as D_(EI), D_(EII) . . . etc.).-   J. A tooth can comprise: a rake surface; a relief surface succeeding    the rake surface and having a relief surface width measurable in a    plane perpendicular to the rotation axis (A_(R)); a cutting edge    formed at an intersection of the rake and relief surfaces; a relief    edge spaced apart from the cutting edge and formed at an    intersection of the relief surface and a flute surface of the flute    succeeding the tooth; and a tooth area defined between a first    radial line extending from the cutting edge to the central rotation    axis and a second radial line extending from the central rotation    axis to a nadir of the succeeding flute.-   K. At an axial location in a front half of an effective cutting    length: at least one tooth, can have a radial rake angle smaller    than an average radial rake angle value of a plurality of teeth of    an end mill; and a flute preceding each at least one tooth can have    a helix angle larger than an average helix angle value of a    plurality of flutes of the end mill. Preferably at least two teeth    can have a radial rake angle smaller than an average radial rake    angle value of a plurality of teeth of an end mill; and a flute    preceding each tooth of the at least one tooth can have a helix    angle larger than an average helix angle value of a plurality of    flutes of the end mill. More preferably, the helix angle can be    equal to a largest value of a helix angle range of the plurality of    flutes. Similarly, it is preferable, that the radial rake angle can    be equal to a smallest radial rake angle value of the plurality of    teeth. Most preferably all teeth with a radial rake angle equal to a    smallest radial rake angle value of the plurality of teeth can be    preceded by a flute with a helix angle larger than an average helix    angle value of the plurality of flutes, preferably a largest helix    angle value of the plurality of flutes. Preferably, each flute of a    majority of flutes having a helix angle larger than an average helix    angle value of the plurality of flutes, are succeeded by a tooth    having a radial rake angle smaller than an average rake angle value    of the plurality of teeth.-   L. At an axial location in a front half of an effective cutting    length, at least one tooth of the plurality of teeth can have: a    radial rake angle which is equal to a largest radial rake angle    range of a plurality of teeth; and a flute preceding each at least    one tooth can have a helix angle which is smaller than a largest    helix angle and larger than a smallest helix angle, of a plurality    of flutes.-   M. At an axial location in a front half of an effective cutting    length: at least one tooth of the plurality of teeth can have a    radial rake angle greater than an average radial rake angle value of    a plurality of teeth of an end mill; and a flute preceding each    tooth of the at least one tooth can have a helix angle smaller than    an average helix angle value of a plurality of flutes of the end    mill.-   N. A plurality of teeth can include at least two, preferably three,    and most preferably a majority of, teeth having different radial    rake angles. At least some, and preferably a majority, of the    different radial rake angle values being different from all other    non-identical values by 2° or more. Preferably each radial rake    angle value is different from all other non-identical values in    accordance with the condition: 3°±1°.-   O. A plurality of flutes can have a helix variance of 6° or less. To    clarify, this means that the largest helix angle value and smallest    helix angle value of all of the plurality of flutes differ by 6° or    less. Preferably, all helix angles of an end mill can be within the    range of 35° to 41°. Most preferably, the helix variance is 4° or    less.-   P. Successive flutes can have different helix angles which vary by    3° or less, preferably 2° or less.-   Q. Each of the plurality of flutes can have an increasing depth with    increasing distance from a shank. A flute depth at a rear end of the    end mill can preferably be between 10% to 14% of the diameter    (D_(EV)). A flute depth at a front end of the end mill can    preferably be between 16% to 20% the diameter (D_(EI)).-   R. At an axial location in a front half of an effective cutting    length at least one tooth, preferably at least two teeth, of a    plurality of teeth can have a tooth area greater than an average    tooth area of the plurality of teeth, and a relief surface width    smaller than an average relief surface width value of the plurality    of teeth. However, it may be preferable that at most only a minority    of teeth of the plurality of teeth have a tooth area greater than an    average tooth area of the plurality of teeth, and a relief surface    width smaller than an average relief surface width value of the    plurality of teeth.-   S. An axial location within a front half of the effective cutting    length can preferably be within a front third of the effective    cutting length.-   T. A cutting portion can have an effective cutting length equal to    or greater than 2.5D_(E). Preferably the effective cutting length is    less than 6D_(E). Most preferably the effective cutting length    fulfills the condition (4D_(E)±1D_(E)) with values approaching    4D_(E) being most preferred.-   U. In a rearward direction from a cutting end face, index angles    between each adjacent pair of cutting edges in cross-sections of the    cutting portion can approach equality and subsequently diverge    therefrom. Preferably said index angles can approach equality with    increasing proximity to a middle of the effective cutting length.-   V. Index angles at a front end of an end mill can correspond to    index angles at a rear end of the effective cutting length. A    majority of index angles at a front end of the end mill can be    unequal.-   W. A diameter D_(E) of the end mill can be a constant value    throughout the effective cutting length (ignoring differences    smaller than about 30 microns). Preferably, the end mill diameter    can be largest at the end face and reduce in diameter with    increasing proximity to the shank and amount less than 30 micron.    When interpreting the claims the diameter to be considered should be    the one at the axial location specified or, if not specified, the    diameter at the end face.-   X. A plurality of teeth is preferably equal to or greater than five    teeth. For the applications described above, a high number of teeth,    is at least five. However, increasing the number of teeth reduces    available flute space. According the plurality of teeth is    preferably equal to or less than 11 teeth. Most preferably the    plurality of teeth is equal to 5, 7 or 9 teeth, with 7 teeth being    considered the most preferred number of teeth taking into account    flute space. Preferably the plurality of teeth is an odd number of    teeth for reducing vibration due to non-symmetry.-   Y. All teeth of a plurality of teeth can all be smooth (i.e.    non-serrated). This can allow better workpiece surface finish. By    “serrated” it is meant that multiple peak-crest shapes (although not    necessarily strictly sinusoidal in shape) are formed adjacent to    each other on the tooth. Accordingly, a “smooth” tooth in accordance    with the present specification and claims may still have a single    peak-crest-peak shape (or even a few significantly spaced from each    other, e.g. at a distance greater than a quarter of the effective    cutting length) which functions as a chip breaker and not for rough    cutting which is the purpose of a serrated tooth. This is because an    occasional chip breaker may still allow good surface finish, even    though a smooth tooth without any chip breaker may provide a    slightly better surface finish and may be preferred for some    applications.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the subject matter of the presentapplication, and to show how the same may be carried out in practice,reference will now be made to the accompanying drawings, in which:

FIG. 1 is a side view of an end mill according to the subject matter ofthe present application;

FIG. 2 is a view of a cutting end face of the end mill in FIG. 1, alonga rotation axis A_(R), i.e. at a front end of the end mill;

FIG. 3 is a cross-section view taken along line III-III in FIG. 1,corresponding to an axial location at a front quarter of the effectivecutting length of the cutting portion;

FIG. 4 is a cross-section view taken along line IV-IV in FIG. 1,corresponding to an axial location in the middle of the effectivecutting length of the cutting portion;

FIG. 5 is a cross-section view taken along line V-V in FIG. 1,corresponding to an axial location at a rear quarter of the effectivecutting length of the cutting portion; and

FIG. 6 is a cross-section view taken along line VI-VI in FIG. 1,corresponding to a rear axial location, i.e. a rear end, of theeffective cutting length of the cutting portion.

DETAILED DESCRIPTION

FIGS. 1 and 2 illustrate an end mill 10, typically made of extremelyhard and wear-resistant material such as cemented carbide, configuredfor rotating about a central rotation axis A_(R) which extendslongitudinally through the center thereof.

The central rotation axis A_(R) defines opposite axially forward andrearward directions D_(F), D_(R), and opposite rotational preceding andsucceeding directions D_(P), D_(S), the preceding direction D_(P) beingthe cutting direction.

The end mill 10 comprises a shank portion 12 and a cutting portion 14extending in the forward direction D_(F) therefrom.

The cutting portion 14 extends in the rearward direction D_(R) from acutting end face 16 to a furthermost flute end 18.

The cutting portion 14 is integrally formed with first, second, third,fourth, fifth, sixth and seventh teeth 20A, 20B, 20C, 20D, 20E, 20F, 20Galternated with helically shaped first, second, third, fourth, fifth,sixth and seventh flutes 22A, 22B, 22C, 22D, 22E, 22F, 22G.

To explain relative terminology used herein, for example, the firstflute 22A is adjacent to the first tooth 20A in the preceding direction(D_(P)), and could therefore is described as the flute which precedesthe first tooth 20A. Another example would be that the seventh flute 22Gsucceeds the first tooth 20A, or, alternatively stated, that the firsttooth 20A precedes the seventh flute 22G, etc.

Shown in FIG. 1, each flute 22 has a helix angle H formed with thecentral rotation axis A_(R). It is understood that the helix angles ofthe various flutes need not be the same, and that the helix angle of anygiven flute may not be constant for its entire length along theeffective cutting length L_(E).

An effective cutting length L_(E) of the cutting portion 14 extends fromthe cutting end face 16 to an axial location where tooth relief surfacesare no longer effective, which is visible in this example at the axiallocation designated with the reference character “29” (in this examplethe axial location of the end of the effective cutting length L_(E)coincides with section VI-VI).

The outer edge of the cutting portion 14 is substantially cylindrical.More precisely, noting this is a preference, the diameter D_(E) of theend mill, when magnified to a magnitude of microns, is greater at thecutting end face 16 than at locations closer to the shank 12. Stateddifferently, the diameter D_(E) decreases with increasing proximity tothe shank 12. Thus D_(EI) is larger than D_(ER), which in turn is largerthan D_(EIII), which in turn is larger than D_(EI), which in turn islarger than D_(EV). Also, in some embodiments, the cutting teeth 20A,20B, 20C, 20D, 20E, 20F, 20G can all extend equally radially outwardlyto establish the diameter D_(E).

As shown from the unbroken appearance of the teeth 20 in FIG. 1, theteeth 20 are non-serrated.

In FIG. 2, first, second, third, fourth, fifth, sixth and seventh indexangles IA1, IA2, IA3, IA4, IA5, IA6, IA7 are shown.

Referring to FIG. 1, aside from the cutting end face 16, i.e. the frontof the effective cutting length L_(E), and section VI-VI at the rear endof the effective cutting length L_(E), intermediary axial locations orsections (or views of a plane perpendicular to the central rotation axisA_(R)) have been chosen for explanatory purposes. For example: sectionIII-III corresponds to an axial location or section rearward of thecutting end face 16 by a quarter of the effective cutting length L_(E);section IV-IV corresponds to an axial location or section rearward ofsection III-III by a quarter of the effective cutting length L_(E) andtherefore represents the middle of the effective cutting length L_(E);section V-V corresponding to an axial location or section rearward ofsection IV-IV by a quarter of the effective cutting length L_(E); andsection VI-VI is an axial location or section rearward of section V-V bya quarter of the effective cutting length L_(E).

Accordingly, a front half 24 of the effective cutting length L_(E) isfrom the section IV-IV to the cutting end face 16, and a rear half 26 ofthe effective cutting length L_(E) is from the section IV-IV to thesection VI-VI.

Using FIG. 3 for ease of visibility, some further features areidentified. Each tooth 20 comprises: first, second, third, fourth,fifth, sixth and seventh rake surfaces (28A, 28B, 28C, 28D, 28E, 28F,28G); first, second, third, fourth, fifth, sixth and seventh reliefsurfaces (30A, 30B, 30C, 30D, 30E, 30F, 30G) succeeding each adjacentrake surface 28 and having first, second, third, fourth, fifth, sixthand seventh relief surface widths (W1, W2, W3, W4, W5, W6, W7); first,second, third, fourth, fifth, sixth and seventh cutting edges (32A, 32B,32C, 32D, 32E, 32F, 32G) formed at respective intersections of the rakeand relief surfaces 28, 30; first, second, third, fourth, fifth, sixthand seventh relief edges (34A, 34B, 34C, 34D, 34E, 34F, 34G) at asucceeding end of each relief surface 30; and first, second, third,fourth, fifth, sixth and seventh flute surfaces (36A, 36B, 36C, 36D,36E, 36F, 36G) succeeding each relief edge (34A, 34B, 34C, 34D, 34E,34F, 34G). Each flute surface 36 extends in the succeeding directionD_(S) until it reaches an adjacent first, second, third, fourth, fifth,sixth or seventh nadir (38A, 38B, 38C, 38D, 38E, 38F, 38G).

To explain measurement of the relief surface widths W with a specificexample, the first relief surface W1 is measured from the first cuttingedge 32A to the relief edge 34A, the relief edge 34A in this exampleconstituting a discontinuity point in a plane perpendicular to therotation axis A_(R). To elaborate a radial line is extended from thecentral rotation axis A_(R) to the first cutting edge 32A and a secondline parallel to the radial line is drawn intersecting the relief edge34A, and the distance between the two lines is measured to provide thewidth. As shown, the first relief surface W1 is succeeded by the firstflute surface 36A which has a different slope. It is understood that incross-sections along the effective cutting length L_(E), the reliefsurfaces 30 are recessed from the footprint of the cutting diameterD_(E), except at the cutting edges 32. In a case where the reliefsurface 30 comprises a plurality of sub-relief surfaces (not shown) therelief edge (i.e. the discontinuity in a cross sectional view) whichshould be considered for width measurement is that which is closest tothe nadir of the flute (and not the cutting edge).

Each tooth 20 comprises a tooth area A_(T). The tooth area A_(T) isdefined between a first radial line L_(R1) extending from the cuttingedge 32 to the central rotation axis A_(R) and a second radial lineL_(R2) extending from the central rotation axis A_(R) to the nadir 38succeeding the cutting edge 32. To explain with a specific example, athird tooth area A_(T3), shown for ease of visibility with hatching, isdefined between a first radial line L_(R1) extending from the thirdcutting edge 32C to the central rotation axis A_(R) and a second radialline L_(R2) extending from the central rotation axis A_(R) to the thirdnadir 38C succeeding the third cutting edge 32C.

In the present example, in the section view shown in FIG. 3, the teethwith the largest tooth areas are the second, third and sixth teeth (20B,20C, 20F) (which could be visually appreciated by drawings radial lineson each one as explained with respect to the third tooth 20C in thepreceding paragraph). Each of the second, third and sixth teeth (20B,20C, 20F) have a tooth area A_(T) greater than an average tooth areaA_(μ) (not shown). An average tooth area A_(μ) can be calculated withthe equation A_(μ)=ΣA_(Ti)/n (where Ti represents the value of aspecific tooth area and n is the number of teeth).

The teeth 20 each have a radial rake angle R, measurable between aradial line extending from the central rotation axis A_(R) to thecutting edge 32 and a tangent line L_(T) extending tangentially from theassociated rake surface 28. To explain with a specific example, thefirst radial rake angle R_(A), is measurable between a first radial lineL_(RA) and a first tangent line L_(TA) from the first rake surface 28A.

In the present example, in the section view shown in FIG. 3, the teethwith the smallest radial rake angles are the third and sixth teeth (20C,20F). The teeth with the largest radial rake angles are the second,fourth and seventh teeth (20B, 20D, 20G). The teeth having radial rakeangles larger than the smallest radial rake angles and smaller than thelargest radial rakes angles are the first and fifth teeth (20A, 20E).

In this example, the third and sixth teeth (20C, 20F) have radial rakeangles of 6°, the second, fourth and seventh teeth (20B, 20D, 20G) haveradial rake angles of 12°, and the first and fifth teeth (20A, 20E) haveradial rake angles of 9°. An average radial rake angle R_(μ) can becalculated with the equation R_(μ)=ΣR_(i)/n (where Ri represents thevalue of a specific radial rake angle and n is the number of teeth). Inthis example the average radial rake angle is calculated as follows:R_(μ)=(6+6+12+12+12+9+9)/7=9.43°. Therefore in this example the second,fourth and seventh teeth (20B, 20D, 20G) have radial rake angles greaterthan the average radial rake angle and the remainder of teeth haveradial rake angles smaller than the average radial rake angle.

In the present example, the flutes with the largest helix angles H arethe third and sixth flutes (22C, 22F). The flutes with the smallesthelix angles are the first and fifth flutes (22A, 22E). The fluteshaving helix angles larger than the smallest helix angles and smallerthan the largest helix angles are the second, fourth and seventh flutes(22B, 22D, 22G). In this example, the third and sixth flutes (22C, 22F)have helix angles of 37°, the second, fourth and seventh flutes (22B,22D, 22G) have helix angles of 36°, and the first and fifth flutes (22A,22E) have helix angles of 35°. An average helix angle H_(μ) can becalculated with the equation H_(μ)=ΣH_(i)/n (where Hi represents thevalue of a specific helix angle and n is the number of teeth). In thisexample the average helix angle is calculated as follows:H_(μ)=(37+37+36+36+36+35+35)/7=36°.

Therefore in this example the second, fourth and seventh flutes (22B,22D, 22G) have helix angles equal to the average helix angle, the firstand fifth flutes (22A, 22E) have helix angles smaller than the averagehelix angle, and the third and sixth flutes (22C, 22F) have helix angleslarger than the average helix angle.

Since the third and sixth teeth have radial rake angles that are smallerthan average and their associated third and sixth flutes have helixangles that are larger than average, the third and sixth teeth can beconsidered to have radial rake angles that are negatively correlatedwith their respective associated third and sixth flutes' helix angles.

Each flute 22 has a flute depth F. The flute depth F is measurablebetween the nadir 38 of the associated flute 22 and the diameter D_(E)in the associated sectional view. The flute depth F can increase withincreasing distance from the shank 12.

In the present example, referring to FIG. 2, a first flute depth F6I ofthe sixth flute 22F, is shown at the cutting end face 16, and at thisaxial location has a largest flute depth, when compared with locationscloser to the shank 12. Notably, the first flute depth F6I is measuredbetween the seventh nadir 38G (noting that the nadirs are numbered incommon with the preceding tooth) and the diameter D_(E). The differentflute depths of the sixth flute 22F are exemplified in the remainingdrawings. Each flute depth closer to the shank 12 has a relativelysmaller magnitude than locations closer to the cutting end face 16. Forexample the first flute depth F6I at the cutting end face 16 is deeper(i.e. greater in magnitude than a second flute depth F6II of the sixthflute 22F in FIG. 3. Similarly, the second flute depth F6II is deeperthan a third flute depth F6III in FIG. 4, which in turn is deeper than afourth flute depth F6IV in FIG. 5, which in turn is deeper than a fifthflute depth F6V in FIG. 6.

Reverting to FIG. 2, index angles are shown measurable between cuttingedges 32. For example, a first index angle IA1 is measurable between thefirst cutting edge 32A and the second cutting edge 32B. Similarlysecond, third, fourth, fifth, sixth and seventh index angles (IA2, IA3,IA4, IA5, IA6, IA7) are shown.

In the present example, the first index angle IA1 is equal to 57.4°, thesecond index angle IA2 is equal to 57.9°, the third index angle IA3 isequal to 45.3°, the fourth index angle IA4 is equal to 45°, the fifthindex angle IA5 is equal to 63.9°, the sixth index angle IA6 is equal to45.2°, and the seventh index angle IA7 is equal to 45.3°.

Reverting to FIG. 3, first, second, third, fourth, fifth, sixth andseventh index angles (IB1, IB2, IB3, IB4, IB5, IB6, IB7) also correspondto the first, second, third, fourth, fifth, sixth and seventh flutes(22A, 22B, 22C, 22D, 22E, 22F, 22G) but have different values to thefirst, second, third, fourth, fifth, sixth and seventh index angles(IA1, IA2, IA3, IA4, IA5, IA6, IA7) in FIG. 1 resulting from the unequalhelix values.

Notably, the helix angles and index angles can be advantageouslyconfigured to approach equality (which in this case is 51.4°, i.e. 360°divided by the no. of teeth) at the middle of the effective cuttinglength. That is to say in FIG. 3 the index angles IB are closer to 51.4°than the index angles IA in FIG. 2, and the first, second, third,fourth, fifth, sixth and seventh index angles (IC1, IC2, IC3, IC4, IC5,IC6, IC7) in FIG. 4 are closer, or equal, to 51.4° than in FIG. 3.

Notably, the helix angles and index angles are configured to divergefrom the equal or near equal values at the middle of the effectivecutting length. That is to say in FIG. 5 the index angles (ID1, ID2,ID3, ID4, ID5, ID6, ID7) are further from the value 51.4° than thecorresponding index angles IC in FIG. 4.

The divergence of the index angles from equality can be approximatelythe same (at least in absolute magnitude) in FIGS. 3 and 5, and also inFIGS. 2 and 6.

Test results for the above-described end mill by far surpassedperformance of comparative end mills tested (on steels having a hardnessof 38-65 HRc, with a chip width of up to 10% of the end mill diameter,and at a depth of 4D). A level of surface finish acceptable according toindustry standards for finish is Ra=0.4 μm, and Ra=0.3 μm was achievedeven at a depth of 4D. Similarly the end mill performed successfullyunder trochoidal milling conditions, and even on stainless steel. Whiletesting has not yet been completed, successful testing was achieved evenfor chips of up to 25% of the end mill diameter. Thus far, all testingeven for varied conditions and materials has been successful.

While each of the features undoubtedly contributed to improvedperformance, each of a number of specific improvements are believed toindividually provide improved performance even for different applicationend mills.

For example, one design feature thought to particularly contribute tothe end mill's performance is that at least one, and preferably each, ofthe third and sixth teeth (20C, 20F), which have a radial rake angle of6° (i.e. a smaller radial rake angle value than the average radial rakeangle of 9.43°, and preferably the smallest radial rake angle out of therake angle set of 6°, 9° and 12°) are each preceded by a flute, i.e.third and sixth flutes 22C, 22F having a helix angle of 37° (i.e. ahelix angle value larger than the average helix angle of 36°, andpreferably the largest helix angle value out of the helix angle set of35°, 36° and 37°).

It is also noted that the converse arrangement is not necessarilydetrimental, i.e. a tooth with the largest radial rake angle (i.e. 12°,which reduces radial cutting force required) does not necessarily haveto be associated with a preceding flute having the smallest helix angle(i.e. 35°) but can beneficially be associated with a preceding flute ofa larger helix angle (i.e. 36°, requiring less radial cutting force thana helix angle of 35°).

Yet another design feature providing a notable independent contributionis the provision of radial rake angles with significantly differentvalues. To offset a particularly long effective cutting length andincreasing flute depth, the radial rake angles are different by 2° ormore (and in this example by 3°). It is believed beneficial, however,for the radial rake angle values to not be overly different so as not tooverly vary cutting forces on a particular tooth thereby increasingwear.

For explanative purposes it is noted that the exemplary radial rakeangle set includes seven values, namely 6°, 6°, 12°, 12°, 12°, 9°, 9°.It is noted that one tooth having a radial rake angle value of 9°differs from the teeth having radial rake angles of 6° by 3°, and alsodiffers from the teeth having radial rake angles of 12° by 3°. Howeverit does not differ at all from the other tooth having an identical valueof 9°. It can now be understood that the tooth having a radial rakeangle value of 9°, has a radial rake angle value which differs by atleast 2° (in this case differing by exactly 3°) from all other teethwith non-identical radial rake values (i.e. this statement therebyexcludes the one other tooth having an identical value of 9°).

Such feature is thought to particularly allow difficult to achieve deepshouldering, successfully tested at 4D but believed to be possible to befeasible at up to, and perhaps even more than 6D.

The deep shouldering capability is believed to be assisted by otherdesign features such as the index angle arrangement which on the onehand comprises different index values to reduce vibration and on theother hand converges towards equality at the center of the end mill anddiverges again to not detrimentally space the teeth.

A similar design contribution can be understood by the helix variancebeing tightly restricted to a close set of values (in this case thevariance being a total of 3° between all flutes). While varying helixangles benefits vibration reduction, this variance was restricted toproduce an end mill with a particularly long effective cutting length,and was subsequently compensated with a relatively larger radial rakevariance (radial rake variation typically being believed to be lesseffective in reducing vibration than helix variation).

Similar to other factors (e.g. the radial rake angles, helix angles,index angles), the flute depths are also varied to reduce vibration, butagain within a limited amount to not detriment the end mill.

Yet another design feature incorporated to reduce vibration was to varytooth width (i.e. provision of different relief surface widths). Toothwidths are typically configured to be as large as possible to providenecessary strength for a cutting action and reduction of a tooth widthcould therefore easily be considered detrimental. Nonetheless, to reducevibration this variation was incorporated and offset by reducing therelief surface widths only on teeth with larger tooth areas.

The description above includes an exemplary embodiment which does notexclude non-exemplified embodiments from the claim scope of the presentapplication.

What is claimed is:
 1. A finish end mill configured for rotating about acentral rotation axis (A_(R)) defining opposite axially forward andrearward directions (D_(F), D_(R)), and opposite rotational precedingand succeeding directions (D_(P), D_(S)), the preceding direction(D_(P)) being the cutting direction, the end mill comprising: a shankportion; and a cutting portion extending forward from the shank portionto a cutting end face; the cutting portion comprising: a diameter(D_(E)); an effective cutting length (L_(E)) greater than 2.5D_(E); aplurality of integrally formed teeth; and a plurality of flutesalternating with the plurality of teeth, each flute having a helix angleand a flute depth; each tooth comprising: a rake surface; a reliefsurface succeeding the rake surface and having a relief surface widthmeasurable in a plane perpendicular to the rotation axis (A_(R)); acutting edge formed at an intersection of the rake and relief surfaces;a relief edge spaced apart from the cutting edge and formed at anintersection of the relief surface and a flute surface of the flutesucceeding the tooth; and a tooth area defined between a first radialline extending from the cutting edge to the central rotation axis and asecond radial line extending from the central rotation axis to a nadirof the succeeding flute; wherein: at an axial location in a front halfof the effective cutting length, at least two of the teeth havedifferent radial rake angle values, at least some of the differentradial rake angle values being different from all other non-identicalvalues by 2° or more; and the flute depth of each flute increases withincreasing distance from the shank.
 2. The finish end mill according toclaim 1, wherein, at an axial location in the front half of theeffective cutting length: the teeth have an average tooth area value,with one or more teeth having a smallest tooth area value, and one ormore teeth having a largest tooth area value; the teeth have an averagerelief surface width value, with one or more teeth having a smallestrelief surface width value, and one or more teeth having a largestrelief surface width value; and at least one tooth has a tooth areagreater than the average tooth area value and a relief surface widthsmaller than the average relief surface width value.
 3. The finish endmill according to claim 1, comprising three or more teeth, wherein at anaxial location in the front half of the effective cutting length: atleast three of the teeth have different radial rake angles, and at leastsome of the different radial rake angle values are different from allother non-identical values by 2° or more.
 4. The finish end millaccording to claim 1, wherein, at an axial location in the front half ofthe effective cutting length: the flutes have an average helix anglevalue, with one or more flutes having a smallest helix angle value, andone or more flutes having a largest helix angle value; the teeth have anaverage radial rake angle value, with one or more teeth having asmallest radial rake angle value, and one or more teeth having a largestradial rake angle value; and at least one tooth has a radial rake anglesmaller than the average radial rake angle value and the flute precedingeach such tooth has a helix angle larger than the average helix anglevalue.
 5. The finish end mill according to claim 4, wherein, at an axiallocation in a front half of an effective cutting length: each of atleast two teeth have a radial rake angle smaller than the average radialrake angle value; and said flute preceding each such tooth has a helixangle larger than the average helix angle value.
 6. The finish end millaccording to claim 4, wherein, at an axial location in a front half ofan effective cutting length: said at least one tooth has a radial rakeangle smaller than the average radial rake angle value; and said flutepreceding each such tooth has a helix angle equal to the largest helixangle value.
 7. The finish end mill according to claim 4, wherein, at anaxial location in a front half of an effective cutting length: said atleast one tooth has a radial rake angle equal to the smallest radialrake angle value.
 8. The finish end mill according to claim 4, wherein,at an axial location in a front half of an effective cutting length:each tooth with a radial rake angle equal to the smallest radial rakeangle value is preceded by a flute with a helix angle larger than theaverage helix angle value.
 9. The finish end mill according to claim 8,wherein, at an axial location in a front half of an effective cuttinglength: each tooth with a radial rake angle equal to the smallest radialrake angle value is preceded by a flute with a helix angle equal to thelargest helix angle value.
 10. The finish end mill according to claim 4,wherein, at an axial location in a front half of an effective cuttinglength: a majority of flutes have a helix angle larger than the averagehelix angle value, and each of said majority of flutes is succeeded by atooth having a radial rake angle smaller than the average radial rakeangle value.
 11. The finish end mill according to claim 4, wherein, atan axial location in a front half of an effective cutting length: atleast one tooth has a radial rake angle which is equal to the largestradial rake angle value; and the flute preceding each such tooth has ahelix angle which is smaller than the largest helix angle value andlarger than the smallest helix angle value.
 12. The finish end millaccording to claim 4, wherein at an axial location in a front half of aneffective cutting length: at least one tooth has a radial rake anglegreater than the average radial rake angle value; and the flutepreceding each such tooth has a helix angle smaller than the averagehelix angle value.
 13. The finish end mill according to claim 1, whereinat an axial location in the front half of the effective cutting length:successive flutes of the plurality of flutes have different helix angleswhich vary by 3° or less.
 14. The finish end mill according to claim 1,wherein at an axial location in the front half of the effective cuttinglength: each radial rake angle value is different from all othernon-identical values in accordance with the condition: 3°±1°.
 15. Thefinish end mill according to claim 1, wherein the plurality of flutescan have a helix variance of 6° or less.
 16. The finish end millaccording to claim 1, wherein the effective cutting length L_(E) is lessthan 6D_(E).
 17. The finish end mill according to claim 16, wherein theeffective cutting length L_(E) fulfills the condition:L_(E)=4D_(E)±1D_(E).
 18. The finish end mill according to claim 1,wherein, in a rearward direction from the cutting end face, index anglesbetween each adjacent pair of cutting edges in cross-sections of thecutting portion approach equality and subsequently diverge therefrom.19. The finish end mill according to claim 18, wherein said index anglesapproach equality with increasing proximity to a middle of the effectivecutting length.
 20. The finish end mill according to claim 1, whereinthe diameter D_(E) of the end mill has a constant value throughout theeffective cutting length.
 21. The finish end mill according to claim 1,wherein the plurality of teeth is equal to or greater than five teethand equal to or less than 11 teeth.
 22. The finish end mill according toclaim 21, wherein the plurality of teeth is equal to 5, 7 or 9 teeth.23. The finish end mill according to claim 1, wherein all of the teethare smooth.
 24. The finish end mill according to claim 1, wherein thesmallest radial rake angle is at least 6°.
 25. The finish end millaccording to claim 1, wherein: the end mill has seven teeth; and adifference between the smallest and largest radial rake angles is atleast 6°.
 26. The finish end mill according to claim 1, wherein: the endmill has seven teeth; and an average value for the radial rake angles isat least 9.0.